International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 46, Pages 2443-2451
doi:10.1155/S0161171204312020

The equivalence of Mann iteration and Ishikawa iteration for ψ-uniformly pseudocontractive or ψ-uniformly accretive maps

B. E. Rhoades1 and Ştefan M. Şoltuz2

 1Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USA
2“Tiberiu Popoviciu” Institute of Numerical Analysis, P.O. Box 68-1, Cluj-Napoca 400110, Romania
Received 2 December 2003

Abstract

We show that the Ishikawa iteration and the corresponding Mann iteration are equivalent when applied to ψ-uniformly pseudocontractive or ψ-uniformly accretive maps.